The Role of the Non-linear Terms and the Magnitudes of Terms in the Equations of Motion

1983 ◽  
pp. 44-62 ◽  
Author(s):  
STEPHEN POND ◽  
GEORGE L. PICKARD
Keyword(s):  
Equations Of Motion ◽  
Non Linear

scholarly journals Sensitivity of wavepackets in jets to non-linear effects: the role of the critical layer

2015 ◽  
Author(s):  
Gilles Tissot ◽  
Mengqi Zhang ◽  
Francisco C. Lajús ◽  
André V. Cavalieri ◽  
Peter Jordan ◽  
...  
Keyword(s):  
Critical Layer ◽  
Non Linear ◽  
Linear Effects

scholarly journals A Unified Mathematical Formalism for First to Third Order Dielectric Response of Matter: Application to Surface-Specific Two-Colour Vibrational Optical Spectroscopy

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 153 ◽  
Author(s):  
Christophe Humbert ◽  
Thomas Noblet
Keyword(s):  
Dielectric Response ◽  
Structure And Properties ◽  
Linear Optics ◽  
Third Order ◽  
Mathematical Functions ◽  
Sum Frequency ◽  
Non Linear Optics ◽  
Non Linear ◽  
Light Excitation

To take advantage of the singular properties of matter, as well as to characterize it, we need to interact with it. The role of optical spectroscopies is to enable us to demonstrate the existence of physical objects by observing their response to light excitation. The ability of spectroscopy to reveal the structure and properties of matter then relies on mathematical functions called optical (or dielectric) response functions. Technically, these are tensor Green’s functions, and not scalar functions. The complexity of this tensor formalism sometimes leads to confusion within some articles and books. Here, we do clarify this formalism by introducing the physical foundations of linear and non-linear spectroscopies as simple and rigorous as possible. We dwell on both the mathematical and experimental aspects, examining extinction, infrared, Raman and sum-frequency generation spectroscopies. In this review, we thus give a personal presentation with the aim of offering the reader a coherent vision of linear and non-linear optics, and to remove the ambiguities that we have encountered in reference books and articles.

Modeling the Climber Fall Arrest Dynamics

2005 ◽  
Author(s):  
Lionel Manin ◽  
Jarir Mahfoudh ◽  
Matthieu Richard ◽  
David Jauffres
Keyword(s):  
Dynamic Characteristics ◽  
Equations Of Motion ◽  
Close Approximation ◽  
Non Linear ◽  
The Future ◽  
Safety Recommendations ◽  
Improved Design ◽  
Fall Arrest

Sports and mountaineering activities are becoming more and more popular. Equipment constructors seek to develop products and devices that are easy to use and that take into account all safety recommendations. PETZL and INSA have collaborated to develop a model for the simulation of displacements and efforts involved during the fall of a climber in the “safety chain”. The model is based on the classical equations of motion, in which climber and belayer are considered as rigid masses, while the rope is considered as a series of non-linear stiffness passing through several devices as brakes and runners. The main goal is to predict the forces in the rope and on the return anchor at the first rebound of the fall. Experiments were first performed in order to observe and determine the dynamic characteristics of the rope, and then to validate results stemming from simulations. Several fall configurations are simulated, and the model performs satisfactorily. It also provides a close approximation of the phenomena observed experimentally. The model enables the assessment of the existing equipments and the improved design of the future one.

In search of lost space: The process of space planning through remembering and history

Organization ◽  
2015 ◽  
Vol 23 (1) ◽  
pp. 71-89 ◽  
Author(s):  
Fabio James Petani ◽  
Jeanne Mengis
Keyword(s):  
Production Of Space ◽  
Space Planning ◽  
The Past ◽  
Time Space ◽  
Non Linear ◽  
Over Time ◽  
Contested Narratives

This article explores the role of remembering and history in the process of planning new spaces. We trace how the organizational remembering of past spaces enters the conception (i.e. planning) of a large culture center. By drawing on Henri Lefebvre’s reflections on history, time and memory, we analyze the processual interconnections of his spatial triad, namely between the planned, practiced, and lived moments of the production of space. We find that over time space planning involves recurrent, changing, and contested narratives on ‘lost spaces’, remembering happy spaces of the past that articulate a desire to regain them. The notion of lost space adds to our understanding of how space planning involves, through organizational remembering, a sociomaterial and spatiotemporal work of relating together different spaces and times in non-linear narratives of repetition.

Investigation of Train Dynamics in Passing Through Curves Using a Full Model

Joint Rail ◽  
2004 ◽  
Author(s):  
Mohammad Durali ◽  
Mohammad Mehdi Jalili Bahabadi
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Full Model ◽  
Bogie Frame ◽  
Nonlinear Characteristics ◽  
Train Derailment ◽  
Train Dynamics

In this article a train model is developed for studying train derailment in passing through bends. The model is three dimensional, nonlinear, and considers 43 degrees of freedom for each wagon. All nonlinear characteristics of suspension elements as well as flexibilities of wagon body and bogie frame, and the effect of coupler forces are included in the model. The equations of motion for the train are solved numerically for different train conditions. A neural network was constructed as an element in solution loop for determination of wheel-rail contact geometry. Derailment factor was calculated for each case. The results are presented and show the major role of coupler forces on possible train derailment.

GPR-based novel approach for non-linear aerodynamic modelling from flight data

2018 ◽  
Vol 123 (1259) ◽  
pp. 79-92
Author(s):  
A. Kumar ◽  
A. K. Ghosh
Keyword(s):  
Aerodynamic Force ◽  
Equations Of Motion ◽  
Gaussian Process Regression ◽  
Likelihood Estimation ◽  
Flight Data ◽  
Novel Approach ◽  
Non Linear ◽  
Research Aircraft ◽  
Novel Method ◽  
Aerodynamic Modelling

ABSTRACTIn this paper, a Gaussian process regression (GPR)-based novel method is proposed for non-linear aerodynamic modelling of the aircraft using flight data. This data-driven regression approach uses the kernel-based probabilistic model to predict the non-linearity. The efficacy of this method is examined and validated by estimating force and moment coefficients using research aircraft flight data. Estimated coefficients of aerodynamic force and moment using GPR method are compared with the estimated coefficients using maximum-likelihood estimation (MLE) method. Estimated coefficients from the GPR method are statistically analysed and found to be at par with estimated coefficients from MLE, which is popularly used as a conventional method. GPR approach does not require to solve the complex equations of motion. GPR further can be directed for the generalised applications in the area of aeroelasticity, load estimation, and optimisation.

scholarly journals Peran Pengasuhan Otoritatif Terhadap Patriotisme Remaja: Dengan Mediator Kepuasan Hidup Dan Nasionalisme

2018 ◽  
Vol 24 (3) ◽  
pp. 326
Author(s):  
Agoes Dariyo
Keyword(s):  
Life Satisfaction ◽  
Significant Role ◽  
Quantitative Research ◽  
Statistical Tests ◽  
Authoritative Parenting ◽  
Measuring Instrument ◽  
Non Linear ◽  
Parenting Role ◽  
Role Of Parents

ABSTRACTThis study  aimed to found out the authoritative parenting role of parents to developed  adolescent nationalism and patriotism in the framework of national resilience. Quantitative research by taking data using a Likert scale measuring instrument in the form of questionnaires, namely authoritative parenting, life-satisfaction, nationalism and patriotism. The subjects involved in this study amounted to 186 adolescents (male = 99 and female = 87 female, with an average age of 18.1 years). Furthermore, the collected data were analyzed using statistical tests, namely logarithmic non-linear regression. The results showed that (a) parents' authoritative parenting played a significant role in developing adolescent nationalism and patriotism in the framework of achieving national resilience, (b) authoritative parenting parents played a significant role in achieving teen life satisfaction so that they also developed nationalism and patriotism in the framework of national resilience, (c) youth realized that the state hadfacilitated its citizens to had jobs so that parents were able to meet the needs of life for teenagers. Thus, they as teenagers were aware of being citizens who had nationalism and patriotism in their lives. ABSTRAKPenelitian ini bertujuan mengetahui peran pengasuhan otoritatif  orangtua untuk menumbuhkembangkan sikap nasionalismedan patriotisme remaja  dalam kerangka ketahanan nasional.Penelitian bersifat kuantitatif dengan pengambilan data menggunakan alat ukur skala Likert berupa kuesioner yaitu pola asuh otoritatif, kepuasan hidup, nasionalisme dan patriotisme. Subjek yang terlibat dalam penelitian ini berjumlah 186 remaja (laki-laki = 99 orang dan perempuan = 87 perempuan, dengan rerata usia 18,1 tahun). Selanjutnya, data yang terkumpul dianalisis dengan menggunakan uji statistik yaitu regresi non-linear logaritmik.Hasil penelitian menunjukkan bahwa (a) pola asuh otoritatif orangtuaberperan secara signifikan dalam menumbuh-kembangkan sikap nasionalisme dan patriotismeremaja dalam kerangka mencapai ketahanan nasional, (b) pola asuh otoritatif orangtua berperan secara signifikan dalam mencapai kepuasan hidup remaja sehingga mereka pun akan menumbuhkembangkan sikap nasionalismedan patriotisme dalam kerangka ketahanan nasional, (c) remaja menyadari bahwa negara telah memfasilitasi warganya untuk memiliki pekerjaan sehingga orangtua  mampu memenuhi kebutuhan hidup bagi anak remaja. Dengan demikian,  mereka sebagai remaja sadar untuk menjadi warga-negara yang memiliki sikap nasionalisme dan patriotisme dalam hidupnya.

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